The Islanders were 6-0-2 in the preseason but trailed 2-0 in the first period.
"The regular season is a different level," New York captain John Tavares said. "Starting with myself, none of us were good enough tonight."
Milano scored in his eighth NHL game at 1:07 of the first period for a 1-0 lead from a setup by Oliver Bjorkstrand.
"It's definitely a good feeling scoring against the team I grew up watching," said Milano, who is from Massapequa, New York. "They're a great team, so it makes it extra special."
Atkinson, who led Columbus with 35 goals last season, made it 2-0 at 11:02 off a pass from Panarin that went off Atkinson's left skate. The play was reviewed and it was determined Atkinson did not use a distinct kicking motion.
"His skate's off the ice. That's the rule," Islanders coach Doug Weight said. "If you're guiding it and your skate comes off the ice, that's the danger point, right? That's how it was described and now I'm told it doesn't matter.
"That was surprising to me. It hurt us. We didn't react to it as well as we had in the preseason."
Murray's goal on a delayed penalty at 6:57 of the second made it 3-0.